This solution produces a white ellipsoid surface with transparency so that lines in the back are faded. Then it adds the major circumferential lines by computing them manually.
% Define center and radii
cnt = [0 0 0]; % center point, row vec
xyzR = [1 2 3]; % radii, row vec
% Compute major circumferential lines.
th = linspace(0,2*pi,150)'; % column vec
ex = @(r,c)c+r*cos(th); % r=radius (scalar), c=center (Scalar)
ey = @(r,c)c+r*sin(th); % r=radius (scalar), c=center (Scalar)
ez = @(c)repmat(c,size(th)); % c=center (scalar)
xy = [ex(xyzR(1),cnt(1)), ey(xyzR(2),cnt(2)), ez(cnt(3)) ];
xz = [ex(xyzR(1),cnt(1)), ez(cnt(2)), ey(xyzR(3),cnt(3))];
yz = [ez(cnt(1)), ey(xyzR(2),cnt(2)), ex(xyzR(3),cnt(3))];
% Plot white, partially transparent ellipsoid
clf
[X,Y,Z] = ellipsoid(cnt(1),cnt(2),cnt(3),xyzR(1),xyzR(2),xyzR(3),16);
sh = surf(X,Y,Z,'facecolor','w','EdgeColor','none','FaceAlpha',.33);
hold on;
xlabel('x'); ylabel('y'); zlabel('z')
% Add circumferential lines
plot3(cnt(1), cnt(2), cnt(3), 'ko','MarkerSize',8,'MarkerFaceColor','k') % center point
lw = 2; % line widths
plot3(xy(:,1), xy(:,2), xy(:,3), 'k-','LineWidth',lw)
plot3(xz(:,1), xz(:,2), xz(:,3), 'k-','LineWidth',lw)
plot3(yz(:,1), yz(:,2), yz(:,3), 'k-','LineWidth',lw)
% Add origin lines
endPoints = (cnt + xyzR).*[-1 -1 1];
plot3([cnt(1),endPoints(1)],cnt([2,2]), cnt([3,3]), 'b-','LineWidth',lw)
plot3(cnt([1,1]), [cnt(2),endPoints(2)],cnt([3,3]), 'b-','LineWidth',lw)
plot3(cnt([1,1]), cnt([2,2]),[cnt(3),endPoints(3)], 'b-','LineWidth',lw)
axis equal
view(-60, 23)
grid off
edit: no content change; cleaned up code by aligning xy, xz, yx matrices.
