Trustbank Ltd holds $50,000$ shares of Zinc Ltd as nominee trustees for Sam. Sam transfers $150,000$ shares of Gold Ltd to Trustbank Ltd$.$ stating that he wishes to provide for his children.

$($i$)$ Sam orally directs Trustban to hold $50,000$ shares of Zinc on trust for his three children, Albert, Jane and Charlotte, in such shares as Trustbank Ltd$.$ shall in its absolute discretion appoint. Several months later, for revenue purposes, Trustbank Ltd$.$ makes a written declaration that it holds the shares on trust for the children.

$($ii$)$ Sam orally directs Trustbank Ltd$.$ to transfer $50,000$ Gold Shares to Albert absolutely$,$ which it does.

$($iii$)$ Sam orally directs Trustbank Ltd$.$ to hold $50,000$ of the Gold Ltd$.$shares on trust for Jane. Sam tells Jane that he has done so$,$ and Jane demands that Trustbank Ltd$.$ transfer the shares to her, which it does.

$($iv$)$ Trustbank Ltd$.$ declares that it holds the remaining $50,000$ shares of Gold Ltd$.$ on trust for Charlottte.

Sam dies, leaving his entire estate to his lover, Fred. Fred disputes the validity of the preceding transactions. Discuss.