Facts and Events
While Thomas Tulloch was Bishop of Orkney (which included both the Orkney and Shetland Islands), he appointed the following Tullochs, presumably relatives, to church positions:
In addition, in 1445 Hector Tulloch was appointed Archdeacon of Caithness, in the neighbouring diocese.  Note a different Thomas Tulloch was Archdeacon of Caithness 1428-1437, Dean of Ross 1436-40 and Bishop of Ross 1440-1460x1.p290
Histories of the Northern Isles recall that whilst Thomas Tulloch was Bishop he oversaw the settlement of many Scottish priests in the local churches, including many from his family.
This was seen in the later records which included the following churchmen:
He is stated to have granted in 1438 Kynclune to his brother David de Tulloch, who may have been the same person as the aforementioned Archdeacon of Shetland and/or related to Sir David Tulloch, vicar of Northmaven, Shetland. 
When Thomas Tulloch received Orkney in fief from the King of Norway, one of his sureties was listed as "Nicolas of Tholach", possibly the same person who is listed as the ancestor of the Tullochs of Lambholm. Note this is a different person to Nicolas Tulloch, vicar of Ruthven and sometime Member of Parliament, who lived in the late 1500s.
The Tullochs of Ness could also be descended from this line.
His coat of arms is shown here
Thomas de Tulloch was a 15th-century Scottish prelate. A native of Angus, of the Tullochs of Bonington near Forfar, he was presbyter of the diocese of Brechin until on 19 August 1418, he was provided as Bishop of Orkney by Pope Martin V. On 17 June 1420, he tendered his oath of fealty to Eric, King of Norway, in the church of Vestenkov in Laland, and was given a commission by the king to administer Orkney on behalf of the Norwegian crown.
A payment of 50 gold florins was made by Bishop Tulloch at Rome on 23 March 1433. The reason for this payment is not known. He obtained a safe-conduct from King Henry VI of England in November 1441 for himself and eight followers, in order to go from Flanders to Scotland, thence through England to Rome. He resigned his see on or before 11 December 1461 for his cousin William de Tulloch, and died in 1463.