Sean Roberts was caught despite running from the property he had set tried to send up in flames.
The 33-year-old had earlier subjected one woman to a horrifying four month campaign of stalking - at one stage threatening to set fire to her home - and made threats against two other women.
At his trial a jury heard how Roberts tormented the first woman at addresses across the Capital between February and mid-May 2017.
He bombarded Stacey Togher with text messages demanding she resume a relationship with him before making threatening and abusive phone calls to her.
He also send her a series of text messages and Facebook messages threatening to kill her and her family and to inflict violence on them.
Roberts later stalked Miss Togher before starting the fire in December 2017.
A jury ruled the fire had endangered lives and convicted Roberts of stalking, threatening and abusive behaviour and wilful fireraising following a trial at the High Court in Edinburgh.
Judge Lord Uist is to consider imposing an Order for Lifelong Restriction - similar to a life sentence - and Roberts was remanded in custody meantime.