Lola and Conchita would request an animal. “Start with the claw this time,” they might say, then they’d crowd around their brother. The scissors would snick the blank paper, from which would fall an effortless Newfoundland, a hen or a dove.

‘Woman’ (1961)

Little Pablo never drew an outline before turning out his precocious découpages for his sisters. The tale (whose source is little Pablo himself) offers a useful foreshadowing of the later showman attended by admiring females, but it would just be another piece of folksy Picassiana were it not for the proof offered at Malaga’s Picasso Museum’s new show.

Dated 1890, somewhat yellowed now, the nine-year-old’s tiny paper dog can be seen with spiky fur under the chin, while the dove’s wing is suggested by an artful cut. It’s hard to tell which is more miraculous, the survival of these frail party pieces or the miniaturist bravura of their child creator.

In the city of his birth, Picasso’s Late Sculpture: Woman explores the lifelong relationship the artist had with paper-cutting and folding, and the ways in which this fed into his experiments with sheet metal in the 1950s and 1960s.

Curated by the art historian Elizabeth Cowling, the show is built around “Woman”, a 1961 sheet-metal work from the museum’s own collection. Diminutive, rusty and at first sight somewhat artless, “Woman” is at the centre of some 40 mainly private loans. The result is a succinct lesson in how Picasso painted through sculpture and sculpted through painting.

He began his foray into metal with “Sylvette”, a 1954 head of his latest model. The echo of paper-folding is inescapable. The thin metal sheet has been worked into what looks like the concertina folds of a paper fan, almost – but not quite – flattened back out to give the shallowest of relief. Over the slapdash white ground only a few black lines form Sylvette’s features in profile, imbued with Picasso’s realist instincts: the model’s bony teenage features and her top-heavy pony-tail all take on an apt gawkiness from the angular sheet itself.

“Sylvette” emerged the year Matisse died. Some years before, Picasso had watched the ageing master cutting paper. “A complete world emerged from his hands, full of strength and vitality,” Françoise Gilot reported of the visit. Hung here, Matisse’s “Venus” bears witness to Gilot’s overt – and Picasso’s perhaps rather more sullen – admiration. The goddess is conjured from thin air, her white torso suggested merely by the two blue cut-outs on either side.

‘Sylvette’ (1954)

Picasso’s “Woman” could be said to be part of Matisse’s complex legacy, the younger artist nettled and urged on by his ghost. Where Matisse excels in collage, it is in keeping with the extreme flatness of his earlier compositions. But Picasso, driven to create similarly complete and vital worlds from paper, is on a different tack altogether.

Obsessively discarding and refining paper maquettes of “Woman” – later converted to sheet metal – his manipulation of paper thinness achieves a very different effect from his French rival. Unlike Matisse, what seems to draw Picasso to sheets of paper or metal are their just-about solidity, a three-dimensionality of the shallowest kind.

That “Woman” is Jacqueline Roque seems clear from a 1962 picture, “Bust of a Seated Woman”, both pieces reflecting the same high forehead. “Bust” is a thought-provoking title for a flat work: while the sculpture, “Woman”, plays on its near-insubstantiality, the picture, with its classically Picassian segmented shapes, sets out to build up solidity. It is just one example of genre-bending highlighted so sharply here.

Perennially fascinated by illusion, Picasso had often looked back to the toy theatres he knew as a child, whose elaborate worlds and layers of depth are wrought out of card. One of Picasso’s gift masks on display shows how a few snips in a silver cake box can make a horned, Dionysian creature. Drama and transformation are only a cut and a fold away.

Paper aside, Picasso clearly lacked technical expertise with sculpture. The inclusion here of Julio González’s “The Lovers” (1932) serves as a reminder of his indebtedness to the Spanish sculptor, with whom he enjoyed a brief partnership in the 1930s. “The Lovers” is a hollow bowl of a head partially covered by a thin “face”, a sheet cut out with futurist rectangle shapes – the lovers’ interlinking lips melting into one-headed unity.

Several pieces reveal Picasso’s instinct for ritual, tribal female figures. “Monument” (1957) is a painting of a female head made up with what seem like welded bars under which little figures huddle in obeisance. While never approaching the near-abstraction of González, Picasso gleaned from his compatriot the distancing, hieratic possibilities of metal.

Then there are the eyes. Monocular almonds, or target-like concentric circles, they peer from his more cultic work like all-seeing seraphim. The word “ojo” held, it has been said, particular fascination for Picasso. It not only means “eye” but is also an imperative: “Be careful! Look out!” Hence the reverence with which Picasso treated his sculptures of women, which he scattered on tables, chairs and window sills (and, in one account, dressed with scarves). Bathed in the light from the circular oriels of his windows in La Californie, he took pleasure in the shifting play of shadow and light on these pieces.

Curatorial rules these days forbid such open, free grouping. But in a show that lays bare the complex influences that lasted a lifetime and contains so many intimations of childhood, it’s gratifying to see these household gods in the city where it all began.

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